Browsing by Author "Zhang, Ding"

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Probing the liquid and solid phases in closely spaced two-dimensional systems
(2014) Zhang, Ding; von Klitzing, Klaus (Prof. Dr.)
Gas, liquid and solid phases are the most common states of matter in our daily encountered 3-dimensional space. The school example is the H2O molecule with its phases vapor, water and ice. Interestingly, electrons - with their point-like nature and negative charges - can also organize themselves under certain conditions to bear properties of these three common phases. At relatively high temperature, where Boltzmann statistics prevails, the ensemble of electrons without interactions can be treated as a gas of free particles. Cooling down the system, this electron gas condenses into a Fermi liquid. Finally, as a result of the repulsive Coulomb forces, electrons try to avoid each other by maximizing their distances. When the Coulomb interaction becomes sufficiently strong, a regular lattice emerges - an electron solid. The story however does not end here. Nature has much more in store for us. Electronic systems in fact exhibit a large variety of phases induced by spatial confinement, an external magnetic field, Coulomb interactions, or interactions involving degrees of freedom other than charge such as spin and valley. Here in this thesis, we restrict ourselves to the study of electrons in a 2-dimenisonal (2D) plane. Already in such a 2D electron system (2DES), several distinct states of matter appear: integer and fractional quantum Hall liquids, the 2D Wigner solid, stripe and bubble phases etc.. In 2DES it is sufficient to sweep the perpendicular magnetic field to pass from one of these phases into another. Experimentally, many of these phases can be revealed by simply measuring the resistance. For a quantum Hall state, the longitudinal resistance vanishes, while the Hall resistance exhibits a plateau. The quantum Hall plateau is a manifestation of localization induced by the inevitable sample disorder. Coulomb interaction can also play an important role to localize charges. Even in the disorder-free case, electrons - more precisely quasi-particles in the partially filled Landau levels - can crystallize into a Wigner crystal. The Wigner crystal is bound to get pinned and hence localizes electrons in the bulk. This may cause an increase of the quantum Hall plateau width. To unveil the existence of such a solid, one has to go beyond standard transport investigations. Both microwave and NMR experiments have shown strong evidences for Wigner crystal formation. In Part I of the thesis, we present measurements of a thermodynamic quantity - the chemical potential. We provide further insight into this solid phase by studying the B-field as well as temperature dependence of the electron crystallization. The sensitive technique that we employ to measure the chemical potential is developed on a GaAs heterostructure with two quantum wells. In fact, in the presence of a perpendicular magnetic field this bilayer system hosts a unique quantum Hall state when each layer has a half filled Landau level. An electron residing in one layer can pair up with an empty state in the opposite layer and excitons may form. These excitons are believed to form an exciton condensate under appropriate conditions. Part II of this thesis is devoted to the understanding of this correlated state. We employ a single electron transistor to probe the chemical potential - more directly its derivative with respect to density, the compressibility - around the νtot=1 quantum Hall state. We then compare excitation gap obtained from this approach with the gap determined from thermally activated transport studies. Our results help to clarify the nature of the excitations at νtot=1. Apart from the thermodynamic measurement, we also perform tunneling experiments on the bilayer. A systematic study of the interlayer tunneling on the distance between the two layers is carried out. Also, we investigate the tunneling on a bilayer with a constriction in the center. Interesting phenomena are observed such as an oscillating pattern in the tunneling current as we gradually open the constriction. While some of our results await further clarifications, one can safely conclude that the electronic bilayer offers intriguing physics, even two decades after its debut.